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arXiv · 2508.09406

CAKR: Commutative algebra k-mer representations for genomics

Faisal Suwayyid·Yuta Hozumi·Mushal Zia·JunJie Wee·Hongsong Feng·Guo-Wei Wei
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Abstract

Despite the availability of various sequence analysis models, comparative genomic analysis remains a challenge in genomics, genetics, and phylogenetics. Commutative algebra, a fundamental tool in algebraic geometry and number theory, has rarely been used in data and biological sciences. In this study, we introduce commutative algebra $k$-mer representations as a nonlinear algebraic framework for analyzing genomic sequences. This representation bridges commutative algebra, algebraic topology, combinatorics, and machine learning to establish a mathematical framework for comparative genomic analysis. We evaluate its effectiveness on three tasks including genetic variant classification, phylogenetic tree reconstruction, and viral classification, typically requiring alignment-based, alignment-free, and machine-learning approaches, respectively. In this work, we show that commutative algebra k-mer representations outperform five state-of-the-art sequence analysis methods across twelve primary datasets, with two additional supplementary fragment-placement benchmarks, especially in viral classification, and maintain relatively stable predictive accuracy as dataset size increases, underscoring scalability and robustness.

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Faisal Suwayyid, Yuta Hozumi, Mushal Zia, JunJie Wee, Hongsong Feng, Guo-Wei Wei. 2025-08-13. CAKR: Commutative algebra k-mer representations for genomics. https://arxiv.org/abs/2508.09406

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